Question

I want help, please.
We have a triangle, a circle marked . Center of the circle inscribed in the triangle is connected to the vertex of the triangle and the extended circle marked crossing. From this point of any chord drawn between the two intersecting triangles . And crosses the circumference . Have to prove that the triangle which is inscribed Object Vertices center of the circle , the triangle with the first chord in the chord crossing point and crossing the center of the marked circle , bisect a given line is tangent to the circle marked on it . please, help :)

Answer 1

A picture would be worth a thousand words in this problem.